A Practical Guide to Pseudospectral Methods PDF Download
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Author: Bengt Fornberg
Publisher: Cambridge University Press
ISBN: 9780521645645
Category : Mathematics
Languages : en
Pages : 248
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Book Description
This book explains how, when and why the pseudospectral approach works.
Author: Bengt Fornberg
Publisher: Cambridge University Press
ISBN: 9780521645645
Category : Mathematics
Languages : en
Pages : 248
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Book Description
This book explains how, when and why the pseudospectral approach works.
Author: Bengt Fornberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 231
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Book Description
Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486411834
Category : Mathematics
Languages : en
Pages : 690
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Book Description
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Author: George Rawitscher
Publisher: Springer
ISBN: 3319427032
Category : Science
Languages : en
Pages : 227
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Book Description
This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 0898714656
Category : Mathematics
Languages : en
Pages : 179
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Lloyd N. Trefethen
Publisher: Princeton University Press
ISBN: 0691213100
Category : Mathematics
Languages : en
Pages : 626
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Book Description
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Author: Daniel Zwillinger
Publisher: Gulf Professional Publishing
ISBN: 9780127843964
Category : Mathematics
Languages : en
Pages : 842
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Book Description
This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. For nearly every technique, the book provides: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
Author: Uri M. Ascher
Publisher: SIAM
ISBN: 0898719976
Category : Mathematics
Languages : en
Pages : 574
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Book Description
Offers students a practical knowledge of modern techniques in scientific computing.
Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9780521806152
Category : Mathematics
Languages : en
Pages : 620
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Book Description
Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory terms, delay equations, and differential-algebraic and integral-algebraic equations. Each chapter starts with a self-contained introduction to the relevant theory of the class of equations under consideration. Numerous exercises and examples are supplied, along with extensive historical and bibliographical notes utilising the vast annotated reference list of over 1300 items. In sum, Hermann Brunner has written a treatise that can serve as an introduction for students, a guide for users, and a comprehensive resource for experts.
Author: Detlef H. Mache
Publisher: Springer Science & Business Media
ISBN: 3764373563
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
